Inflated Cauchy Filters - A Way to Construct the Completion of a General Uniform Space

Abstract

Treatises about General Topology that emphasize the notion of uniformity and uniform space find, of course, no difficulty in defining the notion of a complete uniform space and in constructing the completion of a metric space, via its Cauchy sequences. In contrast, constructing the completion of a general uniform space, especially without recourse to pseudometrics, presents itself as somewhat awkward. In this note the notion of an inflated Cauchy filter is proposed as a way to accomplish that. As the author learned later, all that was actually expounded in Bourbaki, Topologie Generale, 1966 edition (where the filters are referred to as minimal Cauchy rather than inflated Cauchy), hence this note was withdrawn by the author.